Being a variety of finitary algebras, \(\mathsf {U_{BA}}\)  preserves sifted colimits and, in particular, reflexive coequalisers [1]}. In the case of \(\mathsf {U_{CABA}}\)  we use that \(\mathbf {CABA}\)  is equivalent to \(\mathbf {Set}^{\mathrm {op}}\)  and that \([-,2]:\mathbf {Set}^{\mathrm {op}}\rightarrow \mathbf {Set}\)  preserves reflexive coequalisers, see [2]}.
